### Abstract

In the Lagrangian fractional step method introduced in this paper, the fluid velocity and pressure are defined on a collection of N fluid markers. At each time step, these markers are used to generate a Voronoi diagram, and this diagram is used to construct finite-difference operators corresponding to the divergence, gradient, and Laplacian. The splitting of the Navier-Stokes equations leads to discrete Helmholtz and Poisson problems, which we solve using a two-grid method. The nonlinear convection terms are modeled simply by the displacement of the fluid markers. We have implemented this method on a periodic domain in the planee. We describe an efficient algorithm for the numerical construction of periodic Voronoi diagrams, and we report on numerical results which indicate that the fractional step method is convergent of first order. The overall work per time step is proportional to N log N.

Original language | English (US) |
---|---|

Pages (from-to) | 397-438 |

Number of pages | 42 |

Journal | Journal of Computational Physics |

Volume | 70 |

Issue number | 2 |

DOIs | |

State | Published - 1987 |

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### ASJC Scopus subject areas

- Computer Science Applications
- Physics and Astronomy(all)

### Cite this

*Journal of Computational Physics*,

*70*(2), 397-438. https://doi.org/10.1016/0021-9991(87)90189-6

**A Lagrangian fractional step method for the incompressible navier-stokes equations on a periodic domain.** / Börgers, Christoph; Peskin, Charles.

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 70, no. 2, pp. 397-438. https://doi.org/10.1016/0021-9991(87)90189-6

}

TY - JOUR

T1 - A Lagrangian fractional step method for the incompressible navier-stokes equations on a periodic domain

AU - Börgers, Christoph

AU - Peskin, Charles

PY - 1987

Y1 - 1987

N2 - In the Lagrangian fractional step method introduced in this paper, the fluid velocity and pressure are defined on a collection of N fluid markers. At each time step, these markers are used to generate a Voronoi diagram, and this diagram is used to construct finite-difference operators corresponding to the divergence, gradient, and Laplacian. The splitting of the Navier-Stokes equations leads to discrete Helmholtz and Poisson problems, which we solve using a two-grid method. The nonlinear convection terms are modeled simply by the displacement of the fluid markers. We have implemented this method on a periodic domain in the planee. We describe an efficient algorithm for the numerical construction of periodic Voronoi diagrams, and we report on numerical results which indicate that the fractional step method is convergent of first order. The overall work per time step is proportional to N log N.

AB - In the Lagrangian fractional step method introduced in this paper, the fluid velocity and pressure are defined on a collection of N fluid markers. At each time step, these markers are used to generate a Voronoi diagram, and this diagram is used to construct finite-difference operators corresponding to the divergence, gradient, and Laplacian. The splitting of the Navier-Stokes equations leads to discrete Helmholtz and Poisson problems, which we solve using a two-grid method. The nonlinear convection terms are modeled simply by the displacement of the fluid markers. We have implemented this method on a periodic domain in the planee. We describe an efficient algorithm for the numerical construction of periodic Voronoi diagrams, and we report on numerical results which indicate that the fractional step method is convergent of first order. The overall work per time step is proportional to N log N.

UR - http://www.scopus.com/inward/record.url?scp=0002772623&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002772623&partnerID=8YFLogxK

U2 - 10.1016/0021-9991(87)90189-6

DO - 10.1016/0021-9991(87)90189-6

M3 - Article

VL - 70

SP - 397

EP - 438

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 2

ER -